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Ques. When I am going East at 10 km per hour a train moving with constant velocity appears to be moving exactly north east. When my velocity is increased to 30 kmph east it appears to be moving north. Q1 what is the velocity of train along north in kmph ? Q2 what is the velocity of train along east in kmph? Q3 at what speed in kmph should I move north so that train appears to be moving exactly south east ?
Ques. When I am going East at 10 km per hour a train moving with constant velocity appears to be moving  exactly north east. When my velocity is increased to 30 kmph east it appears to be moving north.Q1 what is the velocity of train along north in kmph ?Q2 what is the velocity of train along east in kmph?Q3 at what speed in kmph should I move north so that train appears to be moving exactly south east ?


2 years ago

Susmita
425 Points
							Let the train have a velocity$\vec{v} = a i+bj$When you are moving east with speed 10kmph your velocity$\vec{u} = 10i$Relative velocity of train wrt you is$\vec{r} = \vec{v}-\vec{u}=(a-10)i+bj$But as the train appears to move exactly north east so  b/(a-10)=tan45Or,a-10=bNow you are moving east with a speed 30kmph.Now the relative velocity of train$\vec{r'} = \vec{v}-\vec{u}=(a-30)i+bj$But now the train appears to be moving north.So a-30=0So a=30So b=20Trains velocity=30i+20jAlong east its velocity is 30kmph and along north is 20kmph.Now let you move with a velocity uj along north.Relative velocity of train wrt you is$\vec{r} = \vec{v}-\vec{u}=30i+(10-u)j$But you see the train south east.so tan(90+45)=(10-u)/30Or,-1=(10-u)/30u=40kmph

2 years ago
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